KMK uses the "troupe of strolling players" and the play-within-a-play concept; I adore Porter's line "no Theatre Guild attraction are we," as the Lunts' SHREW was coproduced by the Guild.
I've also always assumed that that was a also bit of a playful dig at Rodgers and Hammerstein, as they wrote for the Guild. Porter had a famous quip about being unsure about his ability to write songs for KMK, because R&H had now set the bar so high with their new look at musicals. (I'm sure the real quote is out there.) Porter (assumedly - unless it was the Spewacks) also peppered the script with digs at the incongruities of production numbers - "We Sing Of Love" is noted as being a song simply there to change the scene - and the famous comment about it never really being too hot to dance in conjunction with "Too Darn Hot."
And of course the odd thing about the "strolling players" lyric is that you could blink and miss that whole conceit. But it's definitely there.